The speed of biased random walk on percolation clusters

2002/11/19 by Noam Berger, Berger, Noam, Nina Gantert +3 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #math-ph #math.MP #math.PR

paper · pdf · doi:10.48550/arxiv.math/0211303

This is a corrected version where the result is only proved for percolation clusters on Z^2; 23 Pages, 3 Figures

arxiv created 2003/01/17 · arxiv updated 2009/11/30

Abstract

We consider biased random walk on supercritical percolation clusters in \Z². We show that the random walk is transient and that there are two speed regimes: If the bias is large enough, the random walk has speed zero, while if the bias is small enough, the speed of the random walk is positive.

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